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Q.

If water is poured into an inverted hollow cone whose semi-vertical  angle is 30° , then the its depth (measured along axis) increases at the  rate of 1cm/sec, the rate of which the volume of water increases when  the depth is 24 cm.

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a

19π19πcm3/sec

b

92π cm3/sec

c

192π cm3/sec

d

200π cm3/sec

answer is C.

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Detailed Solution

V=13πr2htan⁡θ=rhV=π3×h2tan2⁡θhdvdt=π3tan2⁡θ3h2dhdt=πh2tan2⁡θdhdt=π(24)2tan2⁡30∘ (1) cm3/sec=π(24)(24)×13=192πcm3/sec
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